You may, but as there is some difference in their meanings .
보람 is a feeling, some kind of pride, satisfaction one would feel upon doing a deed, but worth is some abstract concept of value or quality.
가치 is probably close to the definition of worth.
Let's say John volunteered to aid to a place where thousands people are hurt in a natural disaster.
His time spent as volunteer wass well worthwhile as he was able to save many people. Hence his action was 가치 있는 행동.
At the same time he felt good and proud of himself for being able to assist people needing help. The good feeling he had for doing something worthwhile is called 보람.
The people from the area try to thank John and try to give just him some award, but since he was among hundreds other volunteers he did not feel worthy enough to receive it alone(Let's assume that John is humble person).
Hence one can feel 보람, but he does not necessarily have to feel worthy.
Story is may sound little bit awkward, but I hope it overall gives you some kind of idea to note the subtle difference in meanings.